强Wolfe线搜索下的修正PRP和HS共轭梯度法

马国栋

Improved PRP and HS Conjugate Gradient Methods with the Strong Wolfe Line Search

Guodong Ma

表 1 第一组方法数值试验报告

序号 算例 IPRP VPRP WYL IFR FR 算例名/维数 Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| 1 bdexp 10 3/1/3/0.005/2.27e-48 3/1/3/0.001/6.25e-49 3/1/3/0.000/6.25e-49 3/1/3/0.000/1.06e-48 F/F/F/F/F 2 bdexp 100 3/2/3/0.000/1.33e-82 3/2/3/0.000/1.24e-82 3/2/3/0.000/1.24e-82 3/2/3/0.000/1.23e-82 4/4/4/0.001/8.22e-10 3 bdexp 1000 3/2/3/0.001/4.45e-107 3/2/3/0.001/4.45e-107 3/2/3/0.002/4.45e-107 3/2/3/0.001/4.41e-107 3/2/3/0.001/3.25e-65 4 bdexp 10000 3/2/3/0.009/1.14e-109 3/2/3/0.009/1.14e-109 3/2/3/0.009/1.14e-109 3/2/3/0.009/1.13e-109 3/2/3/0.007/5.74e-104 5 bdexp 20000 3/2/3/0.019/1.07e-109 3/2/3/0.019/1.07e-109 3/2/3/0.018/1.07e-109 3/2/3/0.019/1.07e-109 3/2/3/0.022/8.65e-107 6 exdenschnb 6 18/333/142/0.027/5.87e-06 21/424/199/0.031/2.28e-06 F/F/F/F/F 92/2469/1261/0.120/7.46e-06 F/F/F/F/F 7 exdenschnb 8 18/333/142/0.016/6.77e-06 21/424/198/0.020/2.63e-06 F/F/F/F/F 81/2181/1132/0.103/9.46e-06 F/F/F/F/F 8 himmelbg 200 3/6/7/0.001/7.14e-29 3/6/7/0.001/7.12e-29 3/6/7/0.001/7.12e-29 3/6/7/0.001/7.13e-29 3/6/7/0.001/2.78e-27 9 himmelbg 1000 3/6/7/0.002/1.60e-28 3/6/7/0.001/1.59e-28 3/6/7/0.001/1.59e-28 3/6/7/0.001/1.59e-28 3/6/7/0.001/6.23e-27 10 himmelbg 2000 3/6/7/0.002/2.26e-28 3/6/7/0.002/2.25e-28 3/6/7/0.002/2.25e-28 3/6/7/0.002/2.26e-28 3/6/7/0.002/8.81e-27 11 himmelbg 5000 3/6/7/0.006/3.57e-28 3/6/7/0.004/3.56e-28 3/6/7/0.004/3.56e-28 3/6/7/0.005/3.57e-28 3/6/7/0.003/1.39e-26 12 genquartic 1000 26/527/272/0.051/8.90e-06 49/1193/591/0.087/1.72e-06 F/F/F/F/F 135/3820/1894/0.262/7.72e-06 F/F/F/F/F 13 genquartic 2000 24/465/195/0.041/3.68e-07 40/829/402/0.071/3.32e-07 F/F/F/F/F 63/1527/759/0.152/4.42e-06 80/1963/985/0.166/8.99e-06 14 genquartic 3000 28/533/256/0.074/9.56e-07 39/819/394/0.110/4.38e-06 130/3558/1746/0.438/2.90e-06 109/2817/1389/0.343/3.04e-06 60/14 36/699/0.198/1.29e-06 15 biggsb1 5 47/1099/508/0.060/3.03e-06 51/1260/580/0.058/3.30e-06 83/2167/1067/0.096/9.24e-06 101/2486/1235/0.114/3.20e-06 116/3006/1485/0.151/1.63e-06 16 biggsb1 10 72/1771/868/0.097/3.99e-06 110/3065/1354/0.176/6.47e-06 321/9146/4502/0.464/6.68e-06 165/4546/2275/0.249/7.11e-06 260/73 83/3699/0.394/7.49e-06 17 sinqua d 3 211/6309/2454/0.327/5.45e-06 141/3934/1661/0.167/8.82e-07 F/F/F/F/F 209/5635/2820/0.292/1.67e-06 F/F/F/F/F 18 fletcbv3 10 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 19 fletcbv3 20 123/2561/1320/0.158/5.54e-06 207/3854/1963/0.230/9.67e-06 144/3777/1938/0.208/9.27e-06 144/3549/1786/0.173/9.18e-06 235/6092/3110/0.287/8.70e-06 20 nonscomp 50 69/1550/742/0.090/5.32e-06 350/10319/4581/0.511/8.98e-06 332/9490/4661/0.474/8.39e-06 F/F/F/F/F F/F/F/F/F 21 dixmaana 1500 15/159/64/0.217/9.53e-07 16/263/115/0.249/2.16e-06 56/1370/656/1.247/7.33e-06 54/1387/654/1.258/6.30e-06 63/1542/738/1.411/8.05e-06 22 dixmaan b 1500 11/140/50/0.145/2.91e-06 11/140/50/0.120/2.90e-06 65/1613/757/1.566/6.91e-06 50/1278/623/1.139/5.80e-06 F/F/F/F/F 23 dixmaanc 1500 60/1667/793/1.578/7.39e-06 21/430/199/0.406/3.25e-06 F/F/F/F/F 141/4104/2008/3.680/1.69e-06 49/1260/611/1.156/8.49e-06 24 dixmaand 1500 63/1757/855/1.670/6.73e-06 F/F/F/F/F 59/1419/655/1.251/8.17e-06 75/1811/888/1.692/2.60e-06 54/1303/644/1.186/8.75e-06 25 dixon3dq 20 521/14809/6503/0.737/4.61e-06 403/11099/5010/0.493/9.85e-06 F/F/F/F/F 411/11043/5496/0.490/8.31e-06 F/F/F/F/F 26 dqdrtic 1000 89/2094/957/0.135/7.15e-06 123/3254/1469/0.195/7.20e-06 337/8603/4223/0.506/8.01e-06 145/3860/1933/0.236/7.33e-06 F/F/F/F/F 27 dqdrtic 3000 115/2569/1149/0.318/2.11e-06 130/3633/1604/0.394/8.77e-06 F/F/F/F/F 267/7418/3623/0.882/4.49e-06 348/9565/4759/1.167/5.93e-06 28 dqrtic 50 17/226/94/0.019/2.87e-06 23/340/152/0.025/9.97e-07 30/571/257/0.039/3.97e-06 37/718/334/0.047/3.17e-06 42/847/422/0.058/3.39e-06 29 dqrtic 100 23/292/117/0.024/9.22e-07 37/740/350/0.059/4.05e-06 39/834/412/0.069/4.43e-06 F/F/F/F/F 56/1250/607/0.100/2.99e-06 30 dqrtic 150 23/345/158/0.035/5.20e-06 27/473/221/0.047/7.25e-06 41/890/411/0.087/7.32e-06 F/F/F/F/F 55/1239/607/0.124/9.64e-06 31 edensch 100 38/805/372/0.075/6.94e-06 37/747/358/0.066/4.94e-06 F/F/F/F/F F/F/F/F/F F/F/F/F/F 32 edensch 200 39/837/402/0.099/7.72e-06 41/894/409/0.103/3.57e-06 586/17937/8632/2.164/6.27e-06 90/2221/1066/0.257/2.92e-06 203/5577/2766/0.698/6.38e-06 33 edensch 1000 53/1251/618/0.559/8.40e-06 57/1412/678/0.604/6.60e-06 212/6028/2941/2.500/9.89e-06 F/F/F/F/F 121/3187/1554/1.336/9.97e-06 34 fletchcr 10 92/2330/1063/0.122/4.66e-06 137/3824/1720/0.198/5.62e-06 181/4817/2375/0.239/9.63e-06 130/3342/1649/0.161/8.36e-06 F/F/F/F/F 35 fletchcr 100 63/1570/739/0.072/4.99e-06 126/3389/1561/0.153/6.47e-06 200/5116/2552/0.272/2.95e-06 136/3723/1839/0.194/8.70e-06 F/F/F/F/F 36 liarwhd 10 85/2053/931/0.126/4.38e-06 118/3128/1461/0.153/6.45e-06 67/1637/822/0.079/7.80e-06 143/3622/1726/0.174/1.86e-06 F/F/F/F/F 37 liarwhd 10 85/2053/931/0.102/4.38e-06 118/3128/1461/0.152/6.45e-06 67/1637/822/0.079/7.80e-06 143/3622/1726/0.175/1.86e-06 F/F/F/F/F 38 liarwhd 20 54/1201/548/0.059/2.51e-06 83/2005/946/0.096/3.67e-06 F/F/F/F/F 112/2678/1341/0.132/6.28e-06 F/F/F/F/F 39 penalt y1 1000 14/243/93/0.755/2.34e-06 14/243/93/0.753/2.34e-06 20/440/186/1.402/8.67e-07 14/243/93/0.702/2.34e-06 F/F/F/F/F 40 penalt y1 2000 10/129/39/1.282/5.53e-06 10/129/39/1.295/5.53e-06 19/421/183/4.409/1.67e-07 13/220/81/2.262/7.43e-07 14/233/82/2.331/1.04e-06 41 power1 30 390/11133/4828/0.479/7.51e-06 F/F/F/F/F F/F/F/F/F 554/14994/7484/0.661/7.38e-06 F/F/F/F/F 42 power1 50 974/27796/12081/1.271/7.98e-06 F/F/F/F/F F/F/F/F/F 844/22960/11507/1.063/7.28e-06 F/F/F/F/F 43 quartc 20 17/218/97/0.015/1.93e-06 25/436/214/0.024/3.39e-06 32/624/296/0.034/5.70e-06 21/369/172/0.022/9.11e-06 21/348/170/0.023/5.01e-06 44 quartc 100 23/292/117/0.034/9.22e-07 37/740/350/0.075/4.05e-06 39/834/412/0.068/4.43e-06 F/F/F/F/F 56/1250/607/0.099/2.99e-06 45 tridia 5 90/2208/1021/0.131/7.47e-06 91/2347/1098/0.111/5.04e-06 233/6288/3116/0.288/9.52e-06 132/3694/1822/0.167/9.45e-06 178/4808 /2347/0.224/8.08e-06 46 raydan2 1000 11/173/64/0.025/6.93e-06 11/173/59/0.015/6.97e-06 13/235/98/0.019/5.88e-06 11/173/64/0.015/6.93e-06 F/F/F/F/F 47 raydan2 5000 15/270/119/0.068/8.63e-07 12/204/71/0.052/8.98e-06 F/F/F/F/F 13/235/81/0.071/7.52e-06 F/F/F/F/F 48 raydan2 9000 13/235/89/0.119/3.57e-06 14/236/80/0.122/8.17e-07 F/F/F/F/F 12/204/73/0.105/9.68e-06 F/F/F/F/F 49 diagonal 1 12 105/3134/1528/0.152/6.47e-06 105/3134/1528/0.138/6.46e-06 178/5045/2412/0.254/8.59e-06 123/3267/1606/0.175/2.63e-06 154/4290/2074/0.188/9.47e-06 50 diagonal 2 20 110/3291/1615/0.167/7.74e-07 112/3352/1629/0.152/1.21e-06 177/4865/2381/0.234/8.10e-06 91/2436/1199/0.109/7.14e-06 158/4381/2169/0.195/6.73e-06 51 diagonal2 100 86/2332/1156/0.125/9.74e-06 138/3993/1881/0.226/5.03e-06 258/7007/3440/0.367/5.18e-06 142/3889/1927/0.228/4.61e-06 314/8540/4265/0.457/3.56e-06 52 diagonal 3 20 94/2642/1291/0.153/4.23e-06 92/2518/1239/0.173/6.97e-06 198/5426/2744/0.254/7.35e-06 136/3671/1808/0.169/8.58e-06 297/8635/4233/0.389/8.19e-06 53 diagonal 3 40 78/1848/864/0.088/8.04e-06 70/1662/798/0.082/2.75e-06 330/9184/4561/0.436/8.35e-06 F/F/F/F/F 166/4212/2153/0.221/7.77e-06 54 bv 1000 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 55 bv 10000 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 56 ie 50 12/193/77/0.255/6.88e-06 11/166/63/0.178/4.87e-06 42/1006/516/1.155/2.93e-06 30/598/294/0.676/7.83e-06 49/1249/599/1.258/9.32e-06 57 ie 200 14/225/98/3.642/3.11e-06 11/166/64/2.631/9.62e-06 58/1475/739/24.086/9.66e-06 42/961/446/15.469/6.32e-06 37/834/424/13.787/4.12e-06 58 gauss 3 8/142/65/0.018/3.85e-06 8/142/64/0.014/3.78e-06 35/912/446/0.082/2.70e-06 5/51/16/0.004/2.43e-06 27/699/363/0.055/3.86e-06 59 kowosb 4 403/11443/5023/0.678/5.35e-06 501/13830/6067/0.789/6.93e-06 F/F/F/F/F 241/6791/3346/0.387/8.22e-06 F/F/F/F/F 60 lin 500 2/2/2/0.021/9.93e-14 2/2/2/0.018/9.93e-14 2/2/2/0.020/9.93e-14 2/2/2/0.016/9.93e-14 2/2/2/0.016/9.93e-14 61 rosex 50 454/13379/5609/0.780/9.65e-06 518/14946/6508/1.015/8.36e-06 F/F/F/F/F F/F/F/F/F F/F/F/F/F 62 trid 20 101/2542/1164/0.206/4.07e-06 111/2785/1293/0.253/4.46e-06 717/20092/10002/1.691/9.73e-06 173/4652/2343/0.360/9.95e-06 449/12935/6383/1.034/9.91e-06 63 vardim 5 10/137/43/0.011/5.41e-07 10/137/43/0.008/5.41e-07 13/228/96/0.013/9.27e-07 10/137/43/0.008/5.41e-07 14/228/88/0.017/5.31e-07 64 watson 4 106/2780/1261/0.345/9.27e-06 190/5428/2430/0.585/9.92e-06 F/F/F/F/F 138/3688/1822/0.368/9.18e-06 F/F/F/F/F